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Strong $k$-transitive oriented graphs with large minimum degree | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 27 بهمن 1402 اصل مقاله (482.97 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.29025.1815 | ||
| نویسنده | ||
| Moussa Daamouch* | ||
| KALMA Laboratory, Department of Mathematics, Faculty of Sciences I, Lebanese University, Beirut, Lebanon | ||
| چکیده | ||
| A digraph $D=(V,E)$ is $k$-transitive if for any directed $uv$-path of length $k$, we have $(u,v) \in E$. In this paper, we study the structure of strong $k$-transitive oriented graphs having large minimum in- or out-degree. We show that such oriented graphs are \emph{extended cycles}. As a consequence, we prove that Seymour's Second Neighborhood Conjecture (SSNC) holds for $k$-transitive oriented graphs for $k \leq 11$. Also we confirm Bermond--Thomassen Conjecture for $k$-transitive oriented graphs for $k \leq 11$. A characterization of $k$-transitive oriented graphs having a hamiltonian cycle for $k \leq 6$ is obtained immediately. | ||
| کلیدواژه‌ها | ||
| k-transitive digraph؛ minimum degree؛ Seymour’ s second neighborhood conjecture؛ Bermond– Thomassen conjecture؛ hamiltonian cycle | ||
| مراجع | ||
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